Towards the Final Generation of Dense Linear Algebra Libraries

Abstract:
What if one set out to develop the final dense linear algebra library?
Such a library would not necessarily have to be backward compatible to existing libraries (although this would be preferred),
but it would have to be forward compatible to future architectures, languages, and functionality.
Invariably such a final generation library would have to be able to generate routines from specification
rather than taking the form of the static libraries that have evolved from EISPACK and LINPACK.
In other words, we believe that the software architecture of such a final generation library would be very different from LAPACK and ScaLAPACK.
In this talk we discuss results from our FLAME project that suggest that mechanical derivation of algorithms from mathematical specification
is achievable, as is the mechanical analysis (cost and stability) and mechanical code generation.
These results suggest that the input to such a system would be the mathematical specifications of operations to be included in the library,
rewrite rules for translating algorithms to code, and models of target architectures.
From this, a full-blown version of the system should then be able to mechanically generate algorithms and implementations,
packaged as libraries tuned on mechanically generated performance analyses, with mechanically generated stability analyses.

Speaker Bio:
Dr. van de Geijn received his PhD in Applied Mathematics from the University of Maryland in 1987, supervised by Professor G. W. (Pete) Stewart.
Since then he has been a faculty member at The University of Texas at Austin.
His interests include software architectures of dense linear algebra libraries, parallel computing, and formal derivation methods.
He has published one book and numerous refereed articles in these areas.